1/4x-2/7=1/2x+2

Solution for 1/4x-2/7=1/2x+2 equation:

1/4x-2/7=1/2x+2

We move all terms to the left:

1/4x-2/7-(1/2x+2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+2)!=0

x∈R


We get rid of parentheses

1/4x-1/2x-2-2/7=0

We calculate fractions


(-32x^2)/392x^2+98x/392x^2+(-196x)/392x^2-2=0

We multiply all the terms by the denominator


(-32x^2)+98x+(-196x)-2*392x^2=0

Wy multiply elements

(-32x^2)-784x^2+98x+(-196x)=0

We get rid of parentheses

-32x^2-784x^2+98x-196x=0

We add all the numbers together, and all the variables

-816x^2-98x=0

a = -816; b = -98; c = 0;
Δ = b2-4ac
Δ = -982-4·(-816)·0
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-98}{2*-816}=\frac{0}{-1632}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+98}{2*-816}=\frac{196}{-1632}
=-49/408
$